I know they require it for backcountry folks, but I don't know about 'cyclists'... there is a 30 minute bear class at the entrance to the park.
Denali bears are not jellystone bears. They do not associate humans with food. If a bear gets food from a human, it is 'schooled' by rangers... with explosives. The rangers care more about the bears than the visitors.
I'm not actually sure under what circumstances you would use pepper spray. As i recall: if you see a bear... you back away. If it sees you, you wave your arms, talk and back away. Here's the funny one; if it charges you, stand there and 'take it'. It will most likely be a bluff charge and they will swerve away. Worst case is you get between mamma and cub, also bad is a sick or mangy bear.
Regardless, the likely hood of any of this happening is remote, just keep your wits about you and don't fly around blind corners. Denali is absolutely amazing and hopefully you get a good view of the mountain.
Our last trip we hiked in through polychrome pass up over the glacier via the valley on the left then came out the right side several days later. We saw tons of caribou, bear, fox and MOSQUITOS.
